(a) Let 𝜈max be the frequency at which the blackbody- radiation function (17.2) is a maximum. Show that 𝜈max= kTx/h, where x is the nonzero solution of x + 3e-x= 3. Since x is a constant, vmax increases linearly with T. (b) Use a calculator with an e* key to solve the equation in (a) by trial and error. To save time, use interpolation after you have found the successive integers that x lies between. Alternatively, use the Solver in Excel, (c) Calculate 𝜈max for a blackbody at 300 K and at 3000 K. Refer to Fig. 20.2 to state in which portions of the electromagnetic spectrum these frequencies lie. (d) The light emitted by the sun conforms closely to the blackbody radiation law and has 𝜈max = 3.5 × 1014 s-1. Estimate the sun's surface temperature. (e) The skin temperature of humans is 33°C, and the emission spectrum of human skin at this temperature conforms closely to black- body radiation. Find 𝜈max for human skin at 33°C. What region of the electromagnetic spectrum is this in?